Anisotropy and dip angle determination using electromagnetic (EM) impulses from tilted antennas

Abstract

Transient responses of a tri-axial resistivity tool corresponding to an electromagnetic (EM) impulse are derived. A transient response of a directional resistivity tool (DRT) corresponding to the EM impulse is derived based on the transient responses of the tri-axial resistivity tool. A theoretical late time transient response of the DRT is derived based on the transient response of the DRT. The late time transient response of the DRT is measured. An anisotropy, a horizontal conductivity, and a dip angle are determined based on the measured late time transient response and the theoretical late time transient response.

What is claimed is: 
     
       1. A computer-implemented method, comprising:
 deriving transient responses of a tri-axial resistivity tool corresponding to an electromagnetic (EM) impulse; 
 deriving a transient response of a directional resistivity tool (DRT) corresponding to the EM impulse based on the transient responses of the tri-axial resistivity tool; 
 deriving a theoretical late time transient response of the DRT based on the transient response of the DRT; 
 measuring the late time transient response of the DRT; and 
 determining an anisotropy, a horizontal conductivity, and a dip angle based on the measured late time transient response and the theoretical late time transient response, including: 
 determining, using a first combination of values of the anisotropy, the horizontal conductivity, and the dip angle, a first error between the measured late time transient response and the theoretical late time transient response; 
 determining, using a second combination of values of the anisotropy, the horizontal conductivity, and the dip angle, a second error between the measured late time transient response and the theoretical late time transient response; and 
 determining the anisotropy, the horizontal conductivity and the dip angle from either the first combination of values or the second combination of values responsive to a comparison of the first error and the second error. 
 
     
     
       2. The method of  claim 1 , wherein the DRT includes one transmitter and one receiver, at least one of a dipole of the transmitter or a dipole of the receiver tilted from a tool axis. 
     
     
       3. The method of  claim 2 , wherein the tri-axial resistivity tool includes three mutually orthogonal transmitters and three mutually orthogonal receivers, the transmitters and the receivers of the tri-axial resistivity tool co-located with the transmitter and the receiver of the DRT, respectively. 
     
     
       4. The method of  claim 1 , wherein deriving the theoretical late time transient response includes having a time in the transient response approach to a large value. 
     
     
       5. The method of  claim 1 , wherein measuring the late time transient response includes measuring the late time transient response at different azimuth angles. 
     
     
       6. The method of  claim 1 , wherein determining the anisotropy, the horizontal conductivity, and the dip angle includes choosing the anisotropy, the horizontal conductivity, and the dip angle such that a difference between the measured late time transient response and the theoretical late time transient response is minimized. 
     
     
       7. The method of  claim 1 , wherein the anisotropy is at least one of a resistivity anisotropy or a conductivity anisotropy. 
     
     
       8. A non-transitory, computer-readable medium storing one or more instructions executable by a computer system to perform operations comprising:
 deriving transient responses of a tri-axial resistivity tool corresponding to an electromagnetic (EM) impulse; 
 deriving a transient response of a directional resistivity tool (DRT) corresponding to the EM impulse based on the transient responses of the tri-axial resistivity tool; 
 deriving a theoretical late time transient response of the DRT based on the transient response of the DRT; 
 measuring the late time transient response of the DRT; and 
 determining an anisotropy, a horizontal conductivity, and a dip angle based on the measured late time transient response and the theoretical late time transient response, including:
 determining, using a first combination of values of the anisotropy, the horizontal conductivity, and the dip angle, a first error between the measured late time transient response and the theoretical late time transient response; 
 determining, using a second combination of values of the anisotropy, the horizontal conductivity, and the dip angle, a second error between the measured late time transient response and the theoretical late time transient response; and 
 determining the anisotropy, the horizontal conductivity and the dip angle from either the first combination of values or the second combination of values responsive to a comparison of the first error and the second error. 
 
 
     
     
       9. The non-transitory, computer-readable medium of  claim 8 , wherein the DRT includes one transmitter and one receiver, at least one of a dipole of the transmitter or a dipole of the receiver tilted from a tool axis. 
     
     
       10. The non-transitory, computer-readable medium of  claim 9 , wherein the tri-axial resistivity tool includes three mutually orthogonal transmitters and three mutually orthogonal receivers, the transmitters and the receivers of the tri-axial resistivity tool co-located with the transmitter and the receiver of the DRT, respectively. 
     
     
       11. The non-transitory, computer-readable medium of  claim 8 , wherein deriving the theoretical late time transient response includes having a time in the transient response approach to a large value. 
     
     
       12. The non-transitory, computer-readable medium of  claim 8 , wherein measuring the late time transient response includes measuring the late time transient response at different azimuth angles. 
     
     
       13. The non-transitory, computer-readable medium of  claim 8 , wherein determining the anisotropy, the horizontal conductivity, and the dip angle includes choosing the anisotropy, the horizontal conductivity, and the dip angle such that a difference between the measured late time transient response and the theoretical late time transient response is minimized. 
     
     
       14. The non-transitory, computer-readable medium of  claim 8 , wherein the anisotropy is at least one of a resistivity anisotropy or a conductivity anisotropy. 
     
     
       15. A computer system, comprising:
 a computer memory; and 
 a hardware processor interoperably coupled with the computer memory and configured to perform operations comprising:
 deriving transient responses of a tri-axial resistivity tool corresponding to an electromagnetic (EM) impulse; 
 deriving a transient response of a directional resistivity tool (DRT) corresponding to the EM impulse based on the transient responses of the tri-axial resistivity tool; 
 deriving a theoretical late time transient response of the DRT based on the transient response of the DRT; 
 measuring the late time transient response of the DRT; and 
 determining an anisotropy, a horizontal conductivity, and a dip angle based on the measured late time transient response and the theoretical late time transient response, including:
 determining, using a first combination of values of the anisotropy, the horizontal conductivity, and the dip angle, a first error between the measured late time transient response and the theoretical late time transient response; 
 determining, using a second combination of values of the anisotropy, the horizontal conductivity, and the dip angle, a second error between the measured late time transient response and the theoretical late time transient response; and 
 determining the anisotropy, the horizontal conductivity and the dip angle from either the first combination of values or the second combination of values responsive to a comparison of the first error and the second error. 
 
 
 
     
     
       16. The computer system of  claim 15 , wherein the DRT includes one transmitter and one receiver, at least one of a dipole of the transmitter or a dipole of the receiver tilted from a tool axis. 
     
     
       17. The computer system of  claim 16 , wherein the tri-axial resistivity tool includes three mutually orthogonal transmitters and three mutually orthogonal receivers, the transmitters and the receivers of the tri-axial resistivity tool co-located with the transmitter and the receiver of the DRT, respectively. 
     
     
       18. The computer system of  claim 15 , wherein deriving the theoretical late time transient response includes having a time in the transient response approach to a large value. 
     
     
       19. The computer system of  claim 15 , wherein measuring the late time transient response includes measuring the late time transient response at different azimuth angles. 
     
     
       20. The computer system of  claim 15 , wherein determining the anisotropy, the horizontal conductivity, and the dip angle includes choosing the anisotropy, the horizontal conductivity, and the dip angle such that a difference between the measured late time transient response and the theoretical late time transient response is minimized.